DebtRank: A Microscopic Foundation for Shock Propagation

RESEARCH ARTICLE DebtRank: A Microscopic Foundation for Shock Propagation Marco Bardoscia1*, Stefano Battiston2, Fabio Caccioli3, Guido Caldarelli1,4,5 1 London Institute for Mathematical Sciences, London, United Kingdom, 2 Department of Banking and Finance, University of Zürich, Zürich, Switzerland, 3 Department of Computer Science, University College London, London, United Kingdom, 4 IMT: Institute for Advanced Studies, Lucca, Italy, 5 CNR-ISC: Institute for Complex Systems, Rome, Italy * a11111 Abstract OPEN ACCESS Citation: Bardoscia M, Battiston S, Caccioli F, Caldarelli G (2015) DebtRank: A Microscopic Foundation for Shock Propagation. PLoS ONE 10(6): e0130406. doi:10.1371/journal.pone.0130406 Academic Editor: Matjaz Perc, University of Maribor, SLOVENIA Received: April 21, 2015 Accepted: May 8, 2015 Published: June 19, 2015 Copyright: © 2015 Bardoscia et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: Data is available from Bankscope software. Please see: http://www.bvdinfo. com/en-gb/our-products/company-information/ international-products/bankscope. Funding: MB, SB, and GC acknowledge support from: FET Project SIMPOL (http://www.simpolproject. eu) nr. 610704, FET project DOLFINS (website not available) nr. 640772, and FET IP Project MULTIPLEX nr. 317532 (http://www.multiplexproject. eu). FC acknowledges support from the Economic and Social Research Council (ESRC, http://www. esrc.ac.uk) in funding the Systemic Risk Centre (ES/ K002309/1). SB acknowledges the Swiss National Fund (http://www.snf.ch) Professorship grant nr. The DebtRank algorithm has been increasingly investigated as a method to estimate the impact of shocks in financial networks, as it overcomes the limitations of the traditional default-cascade approaches. Here we formulate a dynamical “microscopic” theory of instability for financial networks by iterating balance sheet identities of individual banks and by assuming a simple rule for the transfer of shocks from borrowers to lenders. By doing so, we generalise the DebtRank formulation, both providing an interpretation of the effective dynamics in terms of basic accounting principles and preventing the underestimation of losses on certain network topologies. Depending on the structure of the interbank leverage matrix the dynamics is either stable, in which case the asymptotic state can be computed analytically, or unstable, meaning that at least one bank will default. We apply this framework to a dataset of the top listed European banks in the period 2008–2013. We find that network effects can generate an amplification of exogenous shocks of a factor ranging between three (in normal periods) and six (during the crisis) when we stress the system with a 0.5% shock on external (i.e. non-interbank) assets for all banks. Introduction The recent economic downturn has made clear that some substantial features of the present financial markets have not been properly considered. Regulators [1–3] and academics [4] pointed out the role played by complexity [5–7] in the little understanding of the crisis, and in particular the lack of a quantitative assessment for the level of interconnectedness. It has been increasingly recognised that the main and simplest way to quantitatively account for the degree of interconnectedness and complexity of financial markets is given by the theoretical framework of complex networks [8–11]. By representing financial institutions as vertices of a graph we can identify the systemically important ones with the most central vertices [12–14]. Furthermore, the evolution of systemic risk can also be modelled by means of dynamical processes on networks [15–20]. PLOS ONE | DOI:10.1371/journal.pone.0130406 June 19, 2015 1 / 13 DebtRank: A Microscopic Foundation for Shock Propagation PP00P1-144689. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. On the one hand, the use of networks makes the quantification and visualisation of interconnectedness possible; on the other hand, and perhaps even more importantly, network effects are also responsible for a more subtle, typically unnoticed but crucial effect: the amplification of distress. Indeed, while diversification archived through a higher level of interconnectedness reduces the individual risk (in the case of independent shocks), it can however increase systemic risk [21–25]. Nevertheless, there is no single topological structure that is the most robust in all situations because market liquidity also matters [26]. All these issues are presently considered by regulators [27] and the notion of interconnectedness has already entered the debate on “Global Systemically Important Banks” (G-SIBs) [28]. When the banking system is represented as a network, usually propagation of shocks takes place only with removal of vertices in the system, i.e. only after default events. This is an important mechanism for contagion between counterparties [14, 29–31], although in practice this channel becomes active only if balance sheets are already quite deteriorated [16] or in combination with other contagion channels, such as those due to fire sales and overlapping portfolios [21, 22, 32, 33]. The DebtRank algorithm [19] was introduced precisely to overcome this limitation, and to account for the incremental build-up of distress in the system, even before the occurrence of defaults. At the “microsocopic” level, every financial institution satisfies a balance sheet identity that links the values of its assets and liabilities to a capital buffer, which is meant to absorb losses. Balance sheets of different banks are interconnected and therefore the mutual interaction between them is expected to play a major role in the emergence of collective properties, as it is usually the case for many diverse complex systems. For example, our result for the stability of the system, i.e. that it depends only on structural properties and not on the initial state, is a clear example of a general property that finds applications in different domains. The original DebtRank [34] helped to shift the attention towards interconnectedness as a crucial driver of systemic risk [35]. In this paper we show that a similar dynamics can be derived from basic accounting principles and from a simple mechanism for the propagation of shocks from borrower banks to lender banks. A limitation of the original DebtRank is that banks pass on distress to their creditors only once, leading in some cases to a significant underestimation of the level of distress in the system. The dynamics proposed here overcomes this limitation by allowing further propagations of s (...truncated)